The thermal conductivity k of a material is a measure of the ability of the material to conduct heat. The thermal diffusivity of a material .alpha., is related to the conductivity k by: EQU .alpha.=k/.rho.c
where .rho. is the density of the material and c is the specific heat capacity of the material. The product .rho.c is the thermal capacitance per unit volume of the material which generally does not vary significantly for materials from the same family such as different kinds of steels. The thermal capacitance per unit volume also generally does not vary appreciably with certain types of engineering processes such as surface hardening.
Thermal diffusivity of a material is a thermophysical parameter which gives direct and indirect information useful in for example modelling of various industrial processes. Specifically, direct knowledge of thermal diffusivity is required in the modelling of cooling and heating of machinery, heat sinks or spreaders and heat resistant coatings for example. Indirect information of thermal diffusivity obtained from thermal analysis is also useful in non-destructive depth profiling of surface modified metals, the curing of reaction-moulding resins and potentially in the in-situ quality control of manufactured metal sheet.
By measuring thermal diffusivity the thermal conductivity can be obtained using equation (1) using tabulated values of .rho.c. Alternatively, measuring thermal conductivity allows calculation of thermal diffusivity. Typically, thermal conductivity of a material is measured using steady state heat flow methods and there are several experimental techniques currently in use. Experimental methods exist for measurement of thermal diffusivity using time-dependent or dynamic heat flow methods. Dynamic methods of measuring thermal diffusivity are in many ways superior to steady state conductivity measurements in that they allow for faster measurement of thermal diffusivity and are relatively insensitive to background fluctuations and boundary losses; see G. Busse and H. G. Walther, in Progress in Photoacoustic and Photothermal Sciences and Technology, edited by A. Mandelis, Vol. 1, Chapter 5, p. 205, (Elsevier, New York, 1991)].
There are essentially two dynamic or time dependent methods for measuring thermal diffusivity. The first is the periodic heat flow method (see for example L. Qian and P. Li, Appl. Opt. 29, 4241, 1990), and the second comprises transient methods as disclosed in W. P. Leung and A. C. Tam, J. Appl. Phys. 56, 153 (1984) and S. B. Peralta, S. C. Ellis, C. Christofides and A. Mandelis, J. Res. Non-Destructive Eval., 3, 69 (1991).
In the periodic heat flow case, a sample of known thickness is irradiated with a harmonically modulated laser beam thereby launching a thermal wave through the sample. The resulting periodic temperature profile at the front or back surface of the sample is monitored at several modulation frequencies f, also known as the frequency scan method. The frequency dependent thermal diffusion length .mu. is given by: ##EQU1## and is related to the phase-lag of the detected temperature wave with respect to the heating source and may be monitored using a lock-in amplifier.
In transient measurement techniques such as pulsed or multi-frequency spectral excitation, a sample of known thickness is irradiated on one side with a laser pulse and the time evolution of the temperature on either side is monitored and the rate of decay of the temperature is related to the diffusivity.
The measurement of photoexcited excess carrier lifetime is useful in characterizing the quality of semiconductor materials and modelling semiconductor devices. Besides the conventional photoconductive technique for carrier lifetime measurement, many recently developed noncontact, nondestructive techniques have drawn particular interest, [D. K. Schroder, Semiconductor Material and Device Characterization (Wiley, New York, 1990); J. W. Orton and P. Blood, The Electrical Characterization of Semiconductors: Measurement of Minority Carrier Properties (Academic, San Diego, 1990)]. Photothermal radiometry (PTR), (S. J. Sheard, M. G. Somekh and T. Hiller, Mater. Sci. Eng. B 5, 101 (1990)], laser/microwave absorption/reflection (LMR), [T. Warabisako, T. Saitoh, T. Motooka and T. Tokuyama, Jpn. J. Appl. Phys. Suppl. 22-1, 557 (1982); J. Waldmeyer, J. Appl. Phys. 63, 1977 (1988); Z. G. Ling and P. K. Ajmera, J. Appl. Phys. 69, 519 (1991)], infrared absorption (IA), [Y. Mada, Jpn. J. Appl. Phys. 18, 2171 (1979); F. Shimura, T. Okui and T. Kusama, J. Appl. Phys. 61, 7168 (1990); A. Buczkowski, G. A. Rozgonyi and F. Shimura, Proc. MRS Spring Conf. (1992)], photoconductance (PC), [T. Tiegje, J. I. Haberman, R. W. Francis and A. K. Ghosh, J. Appl. Phys. 54, 2499 (1983)], or open-circuit voltage decay (OCVD), [U. Lehmann and H. Foll, J. Electrochem. Soc. 135, 2831 (1988)], are among those techniques commonly used for noncontact carrier lifetime studies. In all these methods laser illumination is used to generate excess electron-hole pairs. The resulting signal is detected in the frequency-domain as a function of modulation frequency (in PTR) or in the time-domain as a transient signal (IA, LMR, PC, and OCVD).